Heat a large saucepan over medium-high heat. Add 1 T. of oil and swirl to coat the bottom. When the oil is hot, add the shrimp and sauté, stirring, until the shrimp are pink, about 1 minute. Season with salt and pepper. Transfer the shrimp to a plate and set aside.

Add the remaining tablespoon of oil 1 T. of the butter. When the mixture is hot, add the garlic and onions and sauté until soft, 1-2 minutes. Add the wine, deglaze the pan, and simmer until the liquid has been absorbed by the rice, 2-3 minutes.

Ladle in the stock 1/2 cup at a time, allowing each addition to be absorbed by the rice before adding the next. Continue until the rice is al dente, about 10 minutes. Return the shrimp to the rice, add the basil, remaining 2 T. of butter, and lime juice. Stir. Taste to adjust the seasoning.